For every number x, x = x, not x < x. So, the inequality x < x has no solution.
Since -3x = -3x for every real number, the inequality
[tex]-3x\leq-3x[/tex]
holds for every real number, that is, every number is a solution.
Consider the inequality
[tex]-4+x>-2+x[/tex]
Subtract x on both sides gives -4 > -2, which is not possible.
Hence the inequality - 4 + x > - 2 + x has no solution.
Consider the inequality
[tex]x-2Subtract x on both sides gives -2 < 3, which is true.
Every real number is a solution of the inequality. Hence the inequality has solution.
Thus the inequalities with no solution are: x < x and -4+x>-2+x
